ΓL(1,𝔽₈)×#461 #13054992

order	1344
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product	ΓL(1,𝔽₈)×#461
unambiguous semidirect product	(C₇×#461)⋊C₃

Fitting, Hall	C₇×#461 ⋊ C₃
Sylow	C₇ ⋊ C₃×#461

240 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 224

A minimal faithful permutation representation — 3 generators on 19 points:

(2,3,4)(5,7,6)(9,11)(12,13,15,18)(14,16,19,17);(1,2,3,5,4,6,7)(8,9,10,11);(13,16)(14,19)(17,18)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 4281);